March 13, 2024Open Access

Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups

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Abstract

Abstract We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym (4) is not a homomorphic image of G and Z (S) Z (S) Z (G) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer problem.

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Riccardo Aragona (Wed,) studied this question.

synapsesocial.com/papers/68e74453b6db6435876bd582 https://doi.org/https://doi.org/10.1007/s10474-024-01408-z

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1Coleman Automorphisms of Some Metabelian Groups2022 · 1 citations
2On the Outer Isomorphisms of a Group1913 · 41 citations
3Locally trivial outer automorphisms of finite groups1970 · 12 citations
4Finite Groups with Class-Preserving outer Automorphisms1947 · 49 citations
5On the modular group ring of a 𝑝-group1964 · 68 citations

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